Huang et al. [1]} proposed the semi-local scaling and Coleman et al. [2]} showed that when turbulence intensities are plotted versus the wall-normal coordinate in semi-local units, a collapse is observed across various Mach numbers. Trettel and Larsson [3]} make an improvement of the van Driest [4]} transformation and derive the Trettel-Larsson [3]} transformation based on the semi-local scaling and the constant stress layer assumption. Patel et al. [6]} develop the same transformation based on the observation that the viscous stress in the near-wall region collapses better in the semi-local scaling. This transformation works in channel flows very well, indeed across the entire inner layer.
